Problem: Rewrite as a simplified fraction. ${0.34\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 343.3333...\\ 100x &= 34.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 309}$ ${x = \dfrac{309}{900}} $ ${x = \dfrac{103}{300}} $